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Intertwined order in correlated quantum systems

Project Description

What happens when different kinds of order occur at the same time in the same material? This basic question builds on a long line of studies in trying to understand the structure of matter, which has always been a key goal in physics. Order (such as solidification) emerges from chaos, when temperature is lowered or if a system parameter such as pressure is changed. While familiar examples of magnetism or superconductivity, superfluidity are by now well understood, it is much less clear what happens when multiple orders compete or co-exist in the same material. Once different types of order come in play, different scenarios may occur. They can compete so that only one form of order survives. Alternatively, multiple orders may coexist independently of each other, or they may even intertwine, meaning one type of order can be converted continuously into the other type.
We propose to study the basic question, so far unanswered in general: what is the theoretical framework that could encompass the complex interplay of physical effects in these scenarios?

We propose to study the basic question, so far unanswered in general: what is the theoretical framework that could encompass the complex interplay of physical effects in these scenarios? For instance, the ‘standard theory’ for the superfluid state of 2D layers of helium-4 atoms is the Berezinskii-Kosterlitz-Thouless (BKT) phase, recognised by the 2016 Physics Nobel Prize. But if the superfluid is close to other kinds of order, the BKT theory can fail.
A tantalising glimpse into novel properties of an intertwined system is offered by the experiment on two layers of helium-4 atoms plated on a flat graphite substrate. The surprise was that there is no sign of the signature of the BKT theory, which is a sudden loss of superfluidity at a critical temperature [1]. Our phenomenological modelling suggests that this superfluid is close to becoming a tightly packed solid. We thus hypothesize that the lack of the BKT transition is due to the intertwining of the superfluid and solid (density wave) order parameters, forming a multi-component order parameter with an enhanced non-Abelian symmetry. As such, it costs no energy to ‘rotate’ between a predominantly superfluid order, into the opposite with predominant density wave order, and anything in between. This is analogous to the non-Abelian SU(2) symmetry governing the isotropic Heisenberg magnets: there, the relevant (intertwined) order parameters are the magnetisations in the three spatial directions, and one can freely rotate the magnetic order pointing in any direction in space without energetic barriers.
Very recently, we constructed a simple model that shows such an intertwined superfluid and solid orders [2]. We have predicted a key signature which is the appearance of extra unusual ele- mentary excitations, that lead directly to the superfluid or condensate densities having anomalous temperature dependences reminiscent of the helium system that motivated our work. Unfortunately, the intertwined state here is only metastable, and moreover requires a smooth, long-range interaction, precluding a direct modelling of the helium system of [3]. However, an important step towards long-range interaction was reported recently for experiments in dipolar cold atomic gases [6].
Quite separately, in the field of quantum optics, two groups have recently reported evidence of supersolidity, where superfluidity coexists with solid order in trapped ultra cold atoms [3-4]. This raises the exciting prospect that one can further engineer these systems to enhance the symmetry to an intertwined kind, by eg. using long-range interactions as we suggested.
In summary, we propose to explore the concept of intertwined orders, which can have a broad range of manifestation in diverse quantum many-body systems.

Eligible candidates should have a MSci (or equivalent) degree in Physics, with an interest in theoretical and computational work. Knowledge of quantum mechanics is essential. Familiarity with condensed matter physics is desirable.

Start date: January 2020

Funding Notes

This studentship is funded by the Leverhulme Trust.
The duration of the studentship is 3.5 years.
The funding provides tuition fees at the level of UK home fees. (Students not eligible for home fee status would require extra funding to cover for the difference between home and overseas fees.)
It also provides a stipend equivalent to the stipend offered by a UK research councils. (2019 stipend: GBP17,009)


1. J. Nyeki, A. Phillis, A. Ho, D. Lee, P. Coleman, J. Parpia, B. Cowan and J. Saunders, “Intertwined superfluid and density wave order in two-dimensional 4He”, Nat Phys. 13, 455 (2017).
2. S. Lieu, A.F. Ho, D. K. K. Lee, and P. Coleman, “p-Orbital Superfluid with S5 Manifold”, arXiv:1803.00970 (2018).
3. Jun-Ru Li, Jeongwon Lee, Wujie Huang, Sean Burchesky, Boris Shteynas, Furkan Cagri Top, Alan O. Jamison and Wolfgang Ketterle, “A stripe phase with supersolid properties in spin- orbit-coupled Bose-Einstein condensates”, Nature 543, 91 (2017).
4. J. Leonard, A. Morales, P. Zupancic, T. Esslinger and T. Donner, “Supersolid formation in a quantum gas breaking a continuous translational symmetry”, Nature 543, 87 (2017).

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